Student:
Class:
Date:
Statistical Studies: Sources of Variability
III.C Student Activity Sheet 9: Introduction to Statistical Bias and Variability
Recall Spud Potato Chips one last time. One sample that was “collected” had the results
shown below. If the true mean of all Spud’s bags is really 28.3 grams, as claimed by the
company, this sample appears to have problems. The sample mean is far below the true
mean and, in fact, all the bags are below the true mean.
This discrepancy between a population parameter and a sample statistic is known as
statistical bias, which can result from many different sources. Two broad categories
of statistical bias are biased sampling method and biased statistic.
1. Give an example of a biased sampling method.
2. Sometimes researchers spend vast resources (time, money, effort) to get a great sample
and then still end up with a biased statistic. For example, something could be wrong with
the data collection method. What could happen after selecting the sample (for example,
potato chip bags) and before calculating the statistic that could result in a biased
statistic?
Charles A. Dana Center at The University of Texas at Austin
Advanced Mathematical Decision Making (2010)
Activity Sheet 9, 4 pages
47
Student:
Class:
Date:
Statistical Studies: Sources of Variability
III.C Student Activity Sheet 9: Introduction to Statistical Bias and Variability
If in fact the method of sampling has introduced bias, one reason for this might be that the
sample was actually nonrepresentative of the population (nonrepresentative sampling).
Nonrepresentative sampling is when the sample does not represent the differences in a
population. For example, the students in this class are mainly seniors in high school;
therefore, they do not represent all students in the school. If only the football team or only
the volleyball team were surveyed at most schools, the sample would have all males or all
females.
3. What other situations could be responsible for bias? Provide examples where possible.
4. REFLECTION: Describe a scenario in which different types of sampling methods lead
to different kinds of bias in sampling, including yielding nonrepresentative samples or
samples with undercoverage of a population.
5. Biased statistics can result from a variety of problems during the data collection process.
Record your thoughts or information you have located through research regarding each of
the following sources of statistical bias.
a. Response bias
b. Nonresponse bias
c. Observer effect
d. Wording of questions
e. Placebo effect
Charles A. Dana Center at The University of Texas at Austin
Advanced Mathematical Decision Making (2010)
Activity Sheet 9, 4 pages
48
Student:
Class:
Date:
Statistical Studies: Sources of Variability
III.C Student Activity Sheet 9: Introduction to Statistical Bias and Variability
Recall that a second sample of Spud Potato Chips was “collected,” and the following results
were obtained:
6. Comment on this distribution compared to that of the original Spud’s sample.
7. REFLECTION: This sample of chips is an example of high variability and no statistical
bias. This situation can be a big problem for the manufacturer. People who get bags with
only 22 grams of chips probably do not really care what the mean is—they just care that
they were shorted! Compare the standard deviations that are given for the original
distribution on Page 1 and this distribution.
What are your recommendations for the manufacturer?
Charles A. Dana Center at The University of Texas at Austin
Advanced Mathematical Decision Making (2010)
Activity Sheet 9, 4 pages
49
Student:
Class:
Date:
Statistical Studies: Sources of Variability
III.C Student Activity Sheet 9: Introduction to Statistical Bias and Variability
8. Identify each of the following as high or low statistical bias and high or low
variability.
a.
c.
b.
d.
9. REFLECTION: In your opinion, which graph in Question 8 represents the
worst situation for researchers? Explain your reasoning.
10. EXTENSION: Variability can be caused by natural variability or induced
variability.
Research each, record your findings, and provide some examples.
a. Natural variability
b. Induced variability
Charles A. Dana Center at The University of Texas at Austin
Advanced Mathematical Decision Making (2010)
Activity Sheet 9, 4 pages
50